Kernel-bounded clustering: Achieving the objective of spectral clustering without eigendecomposition

Abstract

The research on spectral clustering (SC) has thus far been pursued on the same track using the same tool of eigendecomposition of a matrix since the idea was first introduced in 1973. Despite its successes, SC has been identified to have fundamental limitations that prevent SC from discovering certain types of clusters, and SC has slow runtime. We offer an alternative path that does not involve the eigendecomposition, and, more broadly, it uses no optimization. The proposed new Kernel-Bounded Clustering (KBC) is a complete metamorphosis in 50 years of research in SC in view of the fact that KBC achieves the same objective of SC without eigendecomposition or optimization. We evaluated KBC on the datasets that have been used to demonstrate the fundamental limitations of SC, genome-wide expression data, large image datasets and many commonly used real-world benchmark datasets. KBC produced better quality clusters than various variants of SC, and it ran six orders of magnitude faster than the traditional SC on a set of 5 million data points.